Environmental Engineering Reference
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set-points. Some controlled and manipulated variables are subjected to operating
constraints which should also be taken into account:
•
A low limit for bias: for an adequate cleaning action, thus reducing gangue en-
trainment.
•
A high limit for bias: to avoid a decrease in the residence time of the valuable
minerals in the collection zone [5].
•
A low limit for wash water flow rate: to ensure froth stability and transport of the
collected particles into the concentrate launder.
•
A high limit for wash water flow rate: to avoid an increase in froth mixing and
short-circuiting leading to a decrease in froth cleaning [86].
•
A low limit for air flow rate: to maintain solids in suspension.
•
A high limit for air flow rate: to avoid hydraulic entrainment and thus concen-
trate grade deterioration, interface loss and presence of large bubbles at the froth
surface.
The proposed control structure is depicted in Figure 6.12. The froth depth (
H
)
can easily be controlled with a PI controller that manipulates the tailings flow rate
set point (
J
t
). Bias rate (
J
b
) and gas hold-up (ε
g
) are controlled with a MPC by
manipulating wash water rate (
J
ww
)andairflow rate (
J
g
) set points while respecting
the above mentioned constraints. Since the gas hold-up is related to the total bubble
surface area available for particle collection, the objective is to increase its value as
much as possible while respecting operational constraints.
Experimental results are illustrated in Figure 6.13 where set points and con-
straints are, respectively, represented by dash and dash-dotted lines. Since a change
of 50 cm in froth depth only produces a 5% change in the collection zone volume
for a 10 m collection zone height, the impact of the froth depth on column optimiza-
tion is not obvious. A constant 80 cm set point value was selected to damp-down
the gangue entrainment [7]. The Figure 6.13 illustrates the performance of the pro-
posed control structure when the gas hold-up set point is increased. Consequently,
the air flow rate is increased which decreases bias rate until it reaches its constraint,
making gas hold-up unable to attain its high value set point. Selecting such a high
unreachable hold-up set point thus maximizes the bubble surface area available for
particle collection while the bias low limit prevents concentrate grade deterioration
due to hydraulic gangue entrainment.
The second example corresponds to a 2
2 multivariable control in a three-phase
system [69]. The experimental set-up was similar to that used in the previous exam-
ple. The pulp feeding the column was 15% solids, a hematite-silica ore provided by
Compagnie Miniere Quebec-Cartier (now Arcelor-Mittal Mines Canada). Although
flotation is not the most common separation technique for iron ore concentration,
this mineral was retained for this work as it is reagent-free and does not oxidize, as is
the case of sulphurs. Solid particles graded 66.1% iron, and have a size distribution
characterized by 82.6% passing 75 m and 68.8% passing 45 m. An inverse flotation
process (silica flotation) at pH of 9.5 was chosen to minimize reagent consumption.
The reagents used were WW82 (starch) for iron depressing, MG83 as silica collec-
tor and MIBC as frother. Gas hold-up and froth depth were the controlled variables
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